There are three stores, every day Steve will buy something from one of the stores. If yesterday Steve went to store 1 .Today probability 0.5 that he will visit store 2, probability 0.25 he will visit store 3, and probability 0.25 for visiting store 1 again. If yesterday Steve went to store 2. Today, probability 0.33 that Steve will go to store 1, and probability 0.67 he will visit store 3. If yesterday Steve went to store 3, then today he will visit store 1 and store 1 or 3 with probability 0.5 and 0.5 respectively. If Steve goes to store 1 today, on average, calculate the days before Steve goes to store 1 again.
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There are three stores, every day Steve will buy something from one of the stores. If yesterday Steve went to store 1 .Today probability 0.5 that he will visit store 2, probability 0.25 he will visit store 3, and probability 0.25 for visiting store 1 again. If yesterday Steve went to store 2. Today, probability 0.33 that Steve will go to store 1, and probability 0.67 he will visit store 3. If yesterday Steve went to store 3, then today he will visit store 1 and store 1 or 3 with probability 0.5 and 0.5 respectively. If Steve goes to store 1 today, on average, calculate the days before Steve goes to store 1 again.
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- 4. From past experience, Anna knows that the probability that her friend will take her to dinner in Orro Resto id 0.7, the probability that they will watch movies is 0.5, and the probability that he will take her to dinner or they will watch movies is 0.9. What is the probability that they will do both? they will do neither? 5. Eight persons enter a supermarket. From the past experience, it is known that 25% of the people entering the supermarket make a purchase. What is the possible values of the random variable X? Construct the probability distribution of X. X P(X=x) What is the probability that 1) at least four persons will make a purchase? 2) two or three persons will make a purchase? 3) a most two persons will make a purchase?GreenLeaf Electronics offers a new gadget that has been gaining popularity. The probability distribution for the number of gadgets sold per day is provided below. Calculate the average number of gadgets sold per day and determine the variance. NUMBER OF GADGETS SOLD PROBABILITY100 0.10200 0.15300 0.25400 0.25500 0.20600 0.05A manager is quite concerned about the recent deterioration of a section of the roof on a building that houses her firm's computer operations. According to her assistant, there are three options which merit consideration: A, B, and C. Moreover, there are three possible future conditions that must be included in the analysis: I, which has a probability of occurrence of .5; II, which has a probability of .3; and III, which has a probability of .2.If condition I materializes, A will cost USD 12,000, B will cost USD 20,000, and C will cost USD 16,000. If condition II materializes, the costs will be USD 15,000 for A, USD 18,000 for B, and USD 14,000 for C. If condition III materializes, the costs will be USD 10,000 for A, USD 15,000 for B, and USD 19,000 for C._____ alternative will yield the most profit_____ is the profit for the said alternative
- A manager is quite concerned about the recent deterioration of a section of the roof on a building that houses her firm’s computer operations. According to her assistant there are three options which merit consideration: A, B, and C. Moreover, there are three possible future conditions that must be included in the analysis: I, which has a probability of occurrence of .5; II, which has a probability of .3; and III, which has a probability of .2. If condition I materializes, A will cost $1500, B will cost $2000, and C will cost $1600. If condition II materializes, the costs will be $1500 for A, $1800 for B, and $1900 for C. If condition III materializes, the costs will be $1000 for A, $1600 for B, and $1900 for C. (A) Draw a decision tree for this problem. (B) Using expected monetary value, which alternative should be chosenA manager is quite concerned about the recent deterioration of a section of the roof on a building that houses her firm's computer operations. According to her assistant there are three options which merit consideration: I, II, and III. Moreover, there are three possible future conditions that must be included in the analysis: A, which has a probability of occurrence of .3; B, which has a probability of .5; and C, which has a probability of .2.If condition A materializes, I will cost $12,000, II will cost $20,000, and III will cost $16,000. If condition B materializes, the costs will be $15,000 for I, $18,000 for II, and $14,000 for III. If condition C materializes, the costs will be $10,000 for I, $15,000 for II, and $19,000 for III.(A) Draw a decision tree for this problem.(B) Using expected monetary value, which alternative should be chosen?A car repair can be performed either on time or late, and either satisfactoryily or unsatisfactorily. The probability of a repair being on time and satisfactory is 0.26. The probability of a repair being on time is 0.74. The probability of a repair being satisfactory is 0.41. What is the probabilityof a repair being late and unsatisfactory?
- Your manager is quite concerned about the recent deterioration of a section of the roof on a building that houses your firm's computer operations. According to your assistant there are three options which merit consideration: A, B, and C. Moreover, there are three possible future conditions that must be included in the analysis: I, which has a probability of occurrence of .5; II, which has a probability of .3; and III, which has a probability of .2. If condition I materializes, A will cost $12,000, B will cost $20,000, and C will cost $16,000. If condition II materializes, the costs will be $15,000 for A, $18,000 for B, and $14,000 for C. If condition III materializes, the costs will be $10,000 for A, $15,000 for B, and $19,000 for C. (A) Draw a decision tree for this problem (B) Using expected monetary value, which alternative should be chosen? Explain your Answer.Alternative Alternative 1 Alternative 2 Alternative 3 State of Nature Outcome 1 ($) 800 500 700 0.62 Probability according to the payoff table? OEMV (Alternative 1) = $900 EMV (Alternative 3) is the highest EMV EMV (Alternative 2) = EMV (Alternative 3) EMV (Alternative 1) is the highest EMV Outcome 2 ($) 1000 1200 900 0.38 Which of the following statements is correct4. Vacation Inns is a chain of hotels operating in the southwestern part of the United States. The company uses a toll-free telephone number to make reservations for any of its hotels. The average time to handle each call is 3 minutes, and an average of 12 calls are received per hour. The probability distribution that describes the arrivals is unknown. Over a period of time it is determined that the average caller spends 6 minutes either on hold or receiving service. Find the average time in the queue, the average time in the system, the average number in the queue, and the average number in the system.
- An expensive piece of equipment is used in the masking operation for semi-conductor manufacture. A capacitor in the equipment fails randomly. The capacitor cost $7.50, but if it burns out while the machine is in use, the production process must be halted. Here the replacement cost is estimated to be $150. Based on past experience, the lifetime distribution of the capacitor is estimated to be Number of Months of Service 1 2 3 4 5 6 Probability of Failure 0.08 0.12 0.16 0.26 0.22 0.16 How often should the capacitors be replaced in order to minimize the expected monthly cost of planned and unplanned replacement?The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, accordingto the following probability distribution. The squad is on duty 24 hours per day, 7 daysper week:Time BetweenEmergency Calls (hr.) Probability1 .052 .103 .304 .305 .206 .051.00 Compute the average time between calls and compare this value with the expected value of the time between calls from the probability distribution. Why are the results different?|At the Pleasant Haven Hotel there are 36 rooms. The profit earned when a room is sold for a night is $53. If Pleasant Haven overbooks, by selling more reservaitions than they have rooms and they end up having a customer whose reservation cannot be fulfilled, the loss to Pleasant Haven is $30 for that customer. Regardless of the number of rooms booked, the probability of one no show is 60% and the probability of 2 no shows is 20%. There is zero probability of more than 2 no shows. For a night when requests are exceeding the 36 rooms, what is the optimal number of reservations to accept? Assume there is no penalty for a customer who does not show up, i.e., Pleasant Haven does not make $53 on a customer that is a no show. What is the expected net for booking each of the following: (Net means profit minus any overbooking loss.) 36 customers 37 customers 38 customers What is the best number of book?